It is instructive to view the problem of entanglement classification from the broader perspective of classifying quantum from non-signalling correlations. In general, non-signalling distributions are far from being quantum [1]}. Considering product quantum observables, a Gleason-type argument restricts non-signalling bipartite correlations to normalised linear functionals that are positive on pure tensors (POPT), yet not necessarily positive [2]}, [3]}, [4]}, [5]}. To further single out quantum correlations among the latter, various additional physical principles have been proposed, see e.g. [6]}. While successful in some instances, none has been shown to recover the quantum state space in general [7]}.
